We report on measurements of the anisotropic dynamical polarizability of Dy near the 626-nm intercombination line, employing modulation spectroscopy in a one-dimensional optical lattice. To eliminate large systematic uncertainties resulting from the limited knowledge of the spatial intensity distribution, we use K as a reference species with accurately known polarizability. This method can be applied independently of the sign of the polarizability, i.e. for both attractive and repulsive optical fields on both sides of a resonance. By variation of the laser polarization we extract the scalar and the tensorial part. To characterize the strength of the transition, we also derive the natural linewidth. We find our result in excellent agreement with literature values, which provide a sensitive benchmark for the accuracy of our method. In addition we demonstrate optical dipole trapping on the intercombination line, confirming the expected long lifetimes and low heating rates. This provides an additional tool to tailor optical potentials for Dy atoms and for the species-specific manipulation of atoms in the Dy-K mixture.